Each view, e.g. "Branches", "Commits", "Changes" is a tab. You can use drag and drop to rearrange them.

In the above screenshot part which colors of the "commit connector lines" you would use for the message text?

You already can do a lot of those commands in the Outgoing or Journal view. What commands you are missing - please create a new topic for each missing command.

What should be displayed in the tooltip? IMHO, this request often comes up from users who did not fully understand how Git branches work (in contrast to other VCS they are NOT tied to the commits).

Reset hard is already there. I reckon you want an easier to understand way to abort a rebase, merge or cherry-pick?

This would require a whole rewrite of the current compare controls.

Where it should be inserted - above or below the other side's block?

The Files view has a large minimum width but a small minimum height. What about moving it above the Changes view?

You already can right-click a repository and open the shell (using a default external tool).